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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Quadrilateral Exercise 27A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
Solution:

Question 2.
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Solution:

Question 3.
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x-20)° and 6(x+3)°. Find
(i) the value of x.
(ii) each angle of the quadrilateral.
Solution:

Question 4.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C

Solution:

Question 5.
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4:5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD.
Solution:

Question 6.
From the following figure find ;
(i) x,
(ii) ∠ABC,
(iii) ∠ACD.
Solution:

Question 7.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ;
∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
Solution:

Question 8.
In the given figure :
∠b = 2a + 15
and ∠c = 3a+5; find the values of b and c.

Solution:

Question 9.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Solution:

Question 10.
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other. Is PS also parallel to QR ?
Solution:

Question 11.
Use the information given in the following figure to find the value of x.
Solution:

Question 12.
The following figure shows a quadrilateral in which sides AB and DC are parallel.
If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Solution:

Quadrilateral Exercise 27B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120°, find angles B and D.
Solution:

Question 2.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.
Solution:

Question 3.
The angles A, B, C and D of a trapezium ABCD are in the ratio 3 : 4 : 5 : 6.
Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer
Solution:

Question 4.
In an isosceles trapezium one pair of opposite sides are ….. to each Other and the other pair of opposite sides are ….. to each other.
Solution:

Question 5.
Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.
Solution:
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Question 6.
Angle A of an isosceles trapezium is 115° ; find the angles B, C and D.
Solution:

Question 7.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
Solution:

Question 8.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
Solution:

Question 9.
The angles A, B, C and D of a quadrilateral are in the ratio 2:3: 2 : 3. Show this quadrilateral is a parallelogram.
Solution:

Question 10.
In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.

If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.
Solution:

Question 11.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.

Solution:

Question 12.
In parallelogram ABCD, ∠A = 90°
(i) What is the measure of angle B.
(ii) Write the special name of the paralleogram.
Solution:

Question 13.
One diagnol of a rectangle is 18 cm. What is the length of its other diagnol?
Solution:

Question 14.
Each angle of a quadrilateral is x + 5°. Find :
(i) the value of x
(ii) each angle of the quadrilateral.
Give the special name of the quadrilateral taken.

Solution:

Question 15.
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
Solution:

Question 16.
The diagnols of a rhombus are 6 .cm and 8 cm. State the angle at which these diagnols intersect.
Solution:

Question 17.
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.

Solution:

Question 18.
Write two conditions that will make the adjoining figure a square.

Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

Triangles Exercise 26A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In each of the following, find the marked unknown angles :


Solution:

Question 2.
Can a triangle together have the following angles ?
(i) 55°, 55° and 80°
(ii) 33°, 74° and 73°
(iii) 85°, 95° and 22°.
Solution:

Question 3.
Find x, if the angles of a triangle are:
(i) x°, x°, x°
(ii) x°, 2x°, 2x°
(iii) 2x°, 4x°, 6x°
Solution:

Question 4.
One angle of a right-angled triangle is 70°. Find the other acute angle.
Solution:

Question 5.
In ∆ABC, ∠A = ∠B = 62° ; find ∠C.
Solution:

Question 6.
In ∆ABC, C = 56°C = 56° ∠B = ∠C and ∠A = 100° ; find ∠B.
Solution:

Question 7.
Find, giving reasons, the unknown marked angles, in each triangle drawn below:


Solution:

Question 8.
Classify the following triangles according to angle :


Solution:

Question 9.
Classify the following triangles according to sides :

Solution:

Triangles Exercise 26B – Selina Concise Mathematics Class 6 ICSE Solutions

Construct traingle ABC, when :
Question 1.
AB = 6 cm, BC = 8 cm and AC = 4 cm.
Solution:

Question 2.
AB = 3.5 cm, AC = 4.8 cm and BC = 5.2 cm.
Solution:

Question 3.
AB = BC = 5 cm and AC = 3 cm. Mea¬sure angles A and C. Is ∠A = ∠C?
Solution:

Question 4.
AB = BC = CA = 4.5 cm. Measure all the angles of the triangle. Are they equal ?
Solution:

Question 5.
AB = 3 cm, BC = 7 cm and ∠B = 90°.
Solution:

Question 6.
AC = 4.5 cm, BC = 6 cm and ∠C = 60°.
Solution:

Question 7.
AC = 6 cm, ∠A = 60“ and ∠C = 45°. Measure AB and BC.
Solution:

Question 8.
AB = 5.4 cm, ∠A = 30° and ∠B = 90°. Measure ∠C and side BC.
Solution:

Question 9.
AB = 7 cm, ∠B = 120° and ∠A = 30°. Measure AC and BC.
Solution:

Question 10.
BC = 3 cm, AC = 4 cm and AB = 5 cm. Measure angle ACB. Give a special name to this triangle.
Solution:

Triangles Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
If each of the two equal angles of an isosceles triangle is 68°, find the third angle.
Solution:

Question 2.
One of the angles of a triangle is 110°, the two other angles are equal. Find their value.
Solution:

Question 3.
The angles of a triangle are in the ratio 3:5: 7. Find each angle.
Solution:

Question 4.
The angles of a triangle are (2x – 30°),(3x – 40°) and (\(\frac { 5 }{ 2 }\)x + 10°) Find the value of x .
Solution:

Question 5.
In each of the following figures, triangle ABC is equilateral and triangle PBC is isosceles. If PBA = 20°; find in each case:
(a) angle PBC.
(b) angle BPC.

Solution:

Question 6.
Construct a triangle ABC given AB = 6 cm, BC = 5 cm and CA = 5.6 cm. From vertex A draw a perpendicular on to side BC. Measure the length of this perpendicular.
Solution:

Question 7.
Construct a triangle PQR, given PQ = 6 cm, ∠P = 60° and ∠Q = 30°. Measure angle R and the length of PR.
Solution:

Question 8.
Construct a triangle ABC given BC = 5 cm, AC = 6 cm and ∠C = 75°. Draw the bisector of the interior angle at A. Let this bisector meet BC at P ; measure BP.
Solution:

Question 9.
Using ruler and a pair compass only, construct a triangle XYZ given YZ = 7 cm, ∠XYZ = 60° and ∠XZY = 45°. Draw the bisectors of angles X and Y.
Solution:

Question 10.
Using ruler and a pair compass only, construct a triangle PQR, given PQ = 5.5 cm, QR = 7.5 cm and RP = 6 cm. Draw the bisectors of the interior angles at P, Q and R. Do these bisectors meet at the same point ?
Solution:

Question 11.
One angle of a triangle is 80° and the other two are in the ratio 3 : 2. Find the unknown angles of the triangle.
Solution:

Question 12.
Find the value of x if ∠A = 32°, ∠B = 55° and obtuse angle AED = 115°.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Profit, Loss and Discount Exercise 9A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the gain or loss percent, if
(i) C.P. = Rs. 200 and S.P.: = Rs. 224
(ii) C.P. = Rs. 450 and S.P. = Rs. 400
(iii) C.P. = Rs. 550 and gain = Rs . 22
(iv) CP. = Rs. 216 and loss = Rs. 72
(v) S.P. = Rs. 500 and loss : = Rs. 100
(vi) S.P. = Rs. 12 and profit = Rs. 4
(vii) C.P. = Rs. 5 and gain = 60 P

Solution:

Question 2.
Find the selling price, if:
(i) C.P. = Rs. 500 and gain = 25%
(ii) C.P. = Rs. 60 and loss = 12 1/2%
(iii) C.P. = Rs. 150 and loss = 20%
(iv) C.P. = Rs. 80 and gain = 2.5%
Solution:

Question 3.
Rohit bought a tape-recorder for Rs. 1,500 and sold it for Rs. 1,800. Calculate his profit or loss percent.
Solution:

Question 4.
An article bought for Rs. 350 is sold at a profit of 20%. Find its selling price.
Solution:

Question 5.
An old machine is bought for Rs. 1,400 and is sold at a loss of 15%. Find its selling price.
Solution:

Question 6.
Oranges are bought at 5 for Rs. 10 and sold at 6 for Rs. 15. Find profit or loss as percent.
Solution:

Question 7.
A certain number of articles are bought at 3 for Rs. 150 and all of them are sold at 4 for Rs. 180. Find the loss or gain as percent.
Solution:

Question 8.
A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.
Solution:

Question 9.
The cost price of an article is Rs. 1,200 and selling price is \(\frac { 5 }{ 4 }\) times of its cost price. Find:
(i) selling price of the article
(ii) profit or loss as percent.
Solution:

Question 10.
The selling price of an article is Rs. 1,200 and cost price is \(\frac { 5 }{ 4 }\) times of its selling price,
find :
(i) cost price of the article ;
(ii) profit or loss as percent.
Solution:

Profit, Loss and Discount Exercise 9B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the cost price, if:
(i) S.P. = Rs. 21 and gain = 5%
(ii) S.P. = Rs. 22 and loss = 12%
(iii) S.P. = Rs. 340 and gain = Rs. 20
(iv) S.P. = Rs. 200 and loss = Rs. 50
(v) S.P. = Re. 1 and loss = 5 p.
Solution:

Question 2.
By selling an article for Rs. 810, a loss of 10 percent is suffered. Find its cost price.
Solution:

Question 3.
By selling a scooter for Rs. 9,200, a man gains 15%. Find the cost price of the scooter.
Solution:

Question 4.
On selling an article for Rs. 2,640, a profit of 10 percent is made. Find
(i) cost price of the article
(ii) new selling price of it, in order to gain 15%
Solution:

Question 5.
A T.V. set is sold for Rs. 6800 at a loss of 15%. Find
(i)cost price of the T.V. set.
(ii)new selling price of it, in order to gain 12%
Solution:

Question 6.
A fruit seller bought mangoes at Rs. 90 per dozen and sold them at a loss of 8 percent. How much will a customer pay for.
(i) one mango
(ii) 40 mangoes
Solution:

Question 7.
By selling two transistors for Rs. 00 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other.
Find :
(i) C.P. of each transistor
(ii) total C.P. and total S.P. of both the transistors
(iii) profit or loss percent on the whole.
Solution:

Question 8.
Mangoes are bought at 20 for Rs. 60. If
they are sold at 33\(\frac { 1 }{ 3 }\) percent profit.
Find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Solution:

Question 9.
Find the cost price of an article, which is sold for Rs. 4050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Solution:

Question 10.
By selling an article for ₹825, a man loses \(\frac { 1 }{ 3 }\) equal to j of its selling price.
Find :
(i) the cost price of the article,
(ii) the profit percent or the loss percent made, if the same article is sold for ₹1265.
Solution:

Question 11.
Find the loss or gain as percent, if the C.P. of 10 articles, all of the same kind, is equal to S.P. of 8 articles.
Solution:

Question 12.
Find the loss or gain as percent, if the C.P. of 8 articles, all of the same kind, is equal to S.P. of 10 articles.
Solution:

Question 13.
The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Solution:

Question 14.
The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Solution:

Question 15.
Hundred oranges are bought for ₹350 and all of them are sold at the rate of ₹48 per dozen. Find the profit percent or loss percent made.
Solution:

Question 16.
Oranges are bought at 100 for ?80 and all of them are sold at ₹80 for ₹100. Find the loss or gain as percent in this transaction.
Solution:

Question 17.
An article is bought for ₹5,700 and ₹1,300 is spent on its repairing, transportion, etc. For how much should this article be sold in order to gain 20% on the whole.
Solution:
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Profit, Loss and Discount Exercise 9C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A machine is marked at ₹5000 and is sold at a discount of 10%. Find the selling price of the machine.
Solution:

Question 2.
shopkeeper marked a dinner set for ₹1000. He sold it at ₹900, what percent discount did he give ?
Solution:

Question 3.
A pair of shoes marked at ₹320, are sold at a discount of 15 percent.
Find :
(i) discount
(ii) selling price of the shoes.
Solution:

Question 4.
The list price of an article is ₹450 and it is sold for ₹360.
Find :
(i) discount
(ii) discount percent
Solution:

Question 5.
A shopkeeper buys an article for₹300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
Solution:

Question 6.
A car is marked at Rs. 50,000. The dealer gives 5% discount on first Rs. 20,000 and 2% discount on the remaining Rs. 30,000.
Find :
(i) the total discount.
(ii) the price charged by the dealer.
Solution:

Question 7.
A dealer buys a T.V. set for Rs. 2500. He marks it at Rs. 3,200 and then gives a discount of 10% on it.
Find :
(i) the selling price of the T.V. set
(ii) the profit percent made by the dealer.
Solution:

Question 8.
A sells his goods at 15% discount. Find the price of an article which is sold for Rs. 680.
Solution:

Question 9.
A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges Rs. 560.
Solution:

Question 10.
An article is bought for Rs. 1,200 and Rs. 100 is spent on its transportation, etc.
Find :
(i) the total C.P. of the article.
(ii) the selling price of it in order to gain 20% on the whole.
Solution:

Question 11.
40 pens are bought at 4 for Rs. 50 and all of them are sold at 5 for Rs. 80
Find :
(i) C.P. of one pen.
(ii) S/P. of one pen.
(iii) Profit made by selling one pen.
(iv) Profit percent made by selling one pen.
(v) C.P. of 40 pens
(vi) S.P. of 40 pens.
(vii) Profit made by selling 40 pens.
(viii) Profit percent made by selling 40 pens. Are the results of parts (iv) and (viii) same? What conclusion do you draw from the above result ?
Solution:

Question 12.
The C.P. of 5 identical articles is equal to S.P. of 4 articles. Calculate the profit percent or loss percent made if all the articles bought are sold.
Solution:

Question 13.
The C.P. of 8 pens is same as S.P. of 10 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold
Solution:

Question 14.
A certain number of articles are bought at Rs. 450 per dozen and all of them are sold at a profit of 20%. Find the S.P. of:
(i) one article
(ii)seven articles.
Solution:

Question 15.
An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines (Including Parallel Lines)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines (Including Parallel Lines)

Properties of Angles and Lines Exercise 25A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two straight lines AB and CD intersect each other at a point O and angle AOC = 50° ; find :
(i) angle BOD
(ii) ∠AOD
(iii) ∠BOC

Solution:

Question 2.
The adjoining figure, shows two straight lines AB and CD intersecting at point P. If ∠BPC = 4x – 5° and ∠APD = 3x + 15° ; find :

(i) the value of x.
(ii) ∠APD
(iii) ∠BPD
(iv) ∠BPC
Solution:

Question 3.
The given diagram, shows two adjacent angles AOB and AOC, whose exterior sides are along the same straight line. Find the value of x.

Solution:

Question 4.
Each figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line.


Solution:

Question 5.
A line segment AP stands at point P of a straight line BC such that ∠APB = 5x – 40° and ∠APC = .x+ 10°; find the value of x and angle APB.
Solution:

Properties of Angles and Lines Exercise 25B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Identify the pair of angles in each of the figure given below :
adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.


Solution:

Question 2.
Each figure given below shows a pair of parallel lines cut by a transversal For each case, find a and b, giving reasons.




Solution:

Question 3.
If ∠1 = 120°, find the measures of : ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. Give reasons.

Solution:

Question 4.
In the figure given below, find the measure of the angles denoted by x,y, z,p,q and r.

Solution:

Question 5.
Using the given figure, fill in the blanks.

Solution:

Question 6.
In the given figure, find the anlges shown by x,y, z and w. Give reasons.

Solution:

Question 7.
Find a, b, c and d in the figure given below :

Solution:

Question 8.
Find x, y and z in the figure given below :

Solution:

Properties of Angles and Lines Exercise 25C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In your note-book copy the following angles using ruler and a pair compass only.

Solution:

Question 2.
Construct the following angles, using ruler and a pair of compass only
(i) 60°
(ii) 90°
(iii) 45°
(iv) 30°
(v) 120°
(vi) 135°
(vii) 15°
Solution:

Question 3.
Draw line AB = 6cm. Construct angle ABC = 60°. Then draw the bisector of angle ABC.
Solution:

Question 4.
Draw a line segment PQ = 8cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the lengths of PR and QR. Is PR = QR ?
Solution:

Question 5.
Draw a line segment AB = 7cm. Mark a point Pon AB such that AP=3 cm. Draw perpendicular on to AB at point P.
Solution:

Question 6.
Draw a line segment AB = 6.5 cm. Locate a point P that is 5 cm from A and 4.6 cm from B. Through the point P, draw a perpendicular on to the line segment AB.
Solution:

Properties of Angles and Lines Exercise 25D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Draw a line segment OA = 5 cm. Use set-square to construct angle AOB = 60°, such that OB = 3 cm. Join A and B ; then measure the length ofAB.
Solution:

Question 2.
Draw a line segment OP = 8cm. Use set-square to construct ∠POQ = 90°; such that OQ = 6 cm. Join P and Q; then measure the length of PQ.
Solution:

Question 3.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses. Measure each angle so obtained and check whether or not the new angles obtained on bisecting ∠ABC are equal.
Solution:

Question 4.
Draw ∠PQR = 75° by using set- squares. On PQ mark a point M such that MQ = 3 cm. On QR mark a point N such that QN = 4 cm. Join M and N. Measure the length of MN.
Solution:

Properties of Angles and Lines Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In the following figures, AB is parallel to CD; find the values of angles x, y and z :

Solution:

Question 2.
In each of the following figures, BA is parallel to CD. Find the angles a, b and c:

Solution:

Question 3.
In each of the following figures, PQ is parallel to RS. Find the angles a, b and c:

Solution:

Question 4.
Two straight lines are cut by a transversal. Are the corresponding angles always equal?
Solution:

Question 5.
Two straight lines are cut by a transversal so that the co-interior angles are supplementary. Are the straight lines parallel?
Solution:

Question 6.
Two straight lines are cut by a transversal so that the co-interior angles are equal. What must be the measure of each interior angle to make the straight lines parallel to each other ?
Solution:

Question 7.
In each case given below, find the value of x so that POQ is straight line


Solution:

Question 8.
in each case, given below, draw perpendicular to AB from an exterior point P

Solution:

Question 9.
Draw a line segment BC = 8 cm. Using set-squares, draw ∠CBA = 60° and ∠BCA = 75°. Measure the angle BAC. Also measure the lengths of AB and AC.
Solution:

Question 10.
Draw a line AB = 9 cm. Mark a point P in AB such that AP=5 cm. Through P draw (using set-square) perpendicular PQ = 3 cm. Measure BQ.
Solution:

Question 11.
Draw a line segment AB = 6 cm. Without using set squares, draw angle OAB = 60° and angle OBA = 90°. Measure angle AOB and write this measurement.
Solution:

Question 12.
Without using set squares, construct angle ABC = 60° in which AB = BC = 5 cm. Join A and C and measure the length of AC.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 8 Percent and Percentage

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 8 Percent and Percentage

Percent and Percentage Exercise 8A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Express each of the following as percent :

Solution :

Question 2.
Express the following percentages as fractions and as decimal numbers :

Solution :

Question 3.
What percent is :
(i) 16 hours of 2 days ?
(ii) 40 paisa of Rs. 2 ?
(iii) 25 cm of 4 metres
(iv) 600 gm of 5 kg ?
Solution :

Question 4.
Find the value of:

Solution :

Question 5.
In a class of 60 children, 30% are girls. How many boys are there ?
Solution :

Question 6.
In an election, two candidates A and B contested. A got 60% of the votes. The total votes polled were 8000. How many votes did each get ?
Solution :

Question 7.
A person saves 12% of his salary every month. If his salary is ₹2,500, find his expenditure.
Solution :

Question 8.
Seeta got 75% marks out of a total of 800. How many marks did she lose ?
Solution :

Question 9.
A shop worth ₹25,000 was insured for 95% of its value. How much would the owner get in case of any mishappening ?
Solution :

Question 10.
A class has 30 boys and 25 girls. What is the percentage of boys in the class ?
Solution :

Question 11.
Express :
(i) 3 \(\frac { 2 }{ 5 }\) as a percent
(ii) 0.0075 as percent
(iii) 3 : 20 as percent
(iv) 60 cm as percent of 1 m 25 cm
(v) 9 hours as a percent of 4 days.
Solution :

Question 12.
(i) Find 2% of 2 hours 30 min.
(ii) What percent of 12 kg is 725 gm?
Solution :

Percent and Percentage Exercise 8B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Deepak bought a basket of mangoes containing 250 mangoes 12% of these were found to be rotten. Of the remaining, 10% got crushed. How many mangoes were in good condition ?
Solution :

Question 2.
In a Maths Quiz of 60 questions, Chandra got 90% correct answers and Ram got 80% correct answers. How many correct answers did each give ?
What percent is Ram’s correct answers to Chandra’s correct answers ?
Solution :

Question 3.
In an examination, the maximum marks are 900. A student gets 33% of the maximum marks and fails by 45 marks. What is the passing mark ? Also, find the pass percentage.
Solution :

Question 4.
In a train, 15% people travel in first class, 35% travel in second class. The balance travel in the A.C. class ? Calculate the percentage of A.C. class travellers ?
Solution :

Question 5.
A boy eats 25% of the cake and gives away 35% of it to his friends. What percent of the cake is still left with him ?
Solution :

Question 6.
What is the percentage of vowels in the English alphabet ?
Solution :

Question 7.

Solution :

Question 8.
The money spent on the repairs of a house was 1% of its value. If the repair, costs Rs. 5,000, find the cost of the house.
Solution :

Question 9.
In a school out of300 students, 70% are girls and 30% are boys. If 30 girls leave and no new boy is admitted, what is the new percentage of girls in the school ?
Solution :

Question 10.
Kumar bought a transistor for Rs. 960. He paid 12 \(\frac { 1 }{ 2 }\) % cash money. The rest he agreed to pay in 12 equal monthly instalments. How much will he pay each month ?
Solution :

Question 11.
An ore contains 20% zinc. How many kg of ore will be required to get 45 kg of zinc ?
Solution :

Percent and Percentage Exercise 8C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The salary of a man is increased from Rs. 600 per month to Rs. 850 per month. Express the increase in salary as percent.
Solution :

Question 2.
Increase :
(i) 60 by 5%
(ii) 20 by 15%
(iii) 48 by 121 %
(iv) 80 by 140%
(v) 1000 by 3.5%
Solution :

Question 3.
Decrease :
(i)80 by 20%
(ii) 300 by 10%
(iii) 50 by 12.5%
Solution :

Question 4.
What number :
(i) When increased by 10% becomes 88 ?
(ii) When increased by 15% becomes 230 ?
(iii) When decreased by 15% becomes 170 ?
(iv) When decreased by 40% becomes 480 ?
(v) When increased by 100% becomes 100 ?
(vi) When decreased by 50% becomes 50 ?
Solution :

Question 5.
The price of a car is lowered by 20% to Rs. 40,000. What was the original price ? Also, find the reduction in price.
Solution :

Question 6.
If the price of an article is increased by 25%, The increase is Rs. 10. Find the new price.
Solution :

Question 7.
If the price of an article is reduced by 10%, the reduction is Rs. 40. What is the old price ?
Solution :

Question 8.
The price of a chair is reduced by 25%. What is the ratio of:
(i) Change in price to the old price.
(ii) Old price to the new price.
Solution :

Question 9.
If x is 20% less than y, find :

Solution :

Question 10.
If x is 30% more than y; find :

Solution :

Question 11.
The weight of a machine is 40 kg. By mistake it was weighed as 40.8 kg. Find the error percent.
Solution :

Question 12.
From a cask, containing 450 litres of petrol, 8% of the petrol was lost by leakage and evaporation. How many litres of petrol was left in the cask ?
Solution :

Question 13.
An alloy consists of 13 parts of copper, 7 parts of zinc and 5 parts of nickel. What is the percentage of each metal in the alloy?
Solution :

Question 14.
In an examination, first division marks are 60%. A student secures 538 marks and misses the first division by 2 marks. Find the total marks of the examination.
Solution :

Question 15.
Out of 1200 pupils in a school, 900 are boys and the rest are girls. If 20% of the boys and 30% of the girls wear spectacles, find :
(i) how many pupils in all, wear spectacles ?
(ii) what percent of the total number of pupils wear spectacles ?
Solution :

Question 16.
Out of 25 identical bulbs, 17 are red, 3 are black and the remaining are yellow. Find the difference between the numbers of red and yellow bulbs and express this difference as percent.
Solution :

Question 17.
A number first increases by 20% and then decreases by 20%. Find the percentage increase or decrease on the whole.
Solution :

Question 18.
A number is first decreased by 40% and then again decreased by 60%. Find the percentage increase or decrease on the whole.
Solution :

Question 19.
If 150% of a number is 750, find 60% of this number.
Solution :

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 23 Fundamental Concepts

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 23 Fundamental Concepts

Fundamental Concepts Exercise 23A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, true or false, if false, correct the statement.
(i) A dot has width but no length.
(ii) A ray has an infinite length only on one side of it.
(iii) A line segment PQ is written as \(\overleftrightarrow { PQ }\) .
(iv) \(\overleftrightarrow { PQ }\)  represents a straight line.
(v) Three points are said to be collinear, if they lie in the same plane.
(vi) Three or more points all lying in the same line, are called collinear points.
Solution:

Question 2.
Write how many lines can be drawn through :
(i) a given point?
(ii) two given fixed points?
(iii) three collinear points?
(iv) three non-collinear points?
Solution:

Question 3.
The shaded region of the given figure shows a plane :
(a) Name :
(i) three collinear points.
(ii) three non-collinear points.
(iii) a pair of intersecting lines.
(b) State whether true or false :
(i) Line DE is contained in the given plane P.
(ii) Lines AB and DE intersect at point C.
(iii) Points D, B and C are collinear.
(iv) Points D, B and E are collinear.
Solution:

Question 4.
Correct the statement, if it is wrong:
(i) A A ray can be extended infinitely on either side.
(ii) A ray has a definite length.
(iii) A line segment has a definite length.
(iv) A line has two end-points.
(v) A ray has only one end point.
Solution:

Question 5.
State true-er false, if false give the correct statement :
(i) A line has a countable number of points in it.
(ii) Only one line can pass through a given point.
(iii) The intersection of two planes is a straight line
Solution:

Question 6.
State, whether the following pairs of lines or rays appear to be parallel or intersecting.


Solution:

Question 7.
Give two examples, from your surroundings, for each of the following:
(i) points
(ii) line segments
(iii) plane surfaces
(iv) curved surfaces.
Solution:

Question 8.
Under what condition will two straight
lines, in the same plane, have :
(i) no point in common.
(ii) only one point in common.
(iii) an infinite number of points in common.
(iv) If possible draw diagrams in support of your answer.
Solution:

Question 9.
Mark two points A and B on a page of your exercise book. Mark a third point P, such that :
(i) P lies between A and B; and the three points A, P and B are collinear.
(ii) P does not lie between A and B yet the three points are collinear.
(iii) the three points do not lie in a line.
Solution:

Question 10.
Mark two points P and Q on a piece of paper. How many lines can you draw:
(i) passing through both the points P and Q?
(ii) passing through the point P ?
(iii) passing through the point Q ?
Solution:

Question 11.
The adjoining diagram shows a line AB. Draw diagram to represent:
(i) ray AB i.e. \(\overrightarrow { AB } \)

(ii) \(\overrightarrow { BA } \)
(iii) line segment AB.
Solution:

Question 12.
The adjoining diagram shows a ray AB. Draw diagrams to show :
(i) ray BA i.e. \(\overrightarrow { BA } \)
(ii) lineAB
(iii) line segment BA.

Solution:

Question 13.
The adjoining diagram shows a line segment AB. Draw diagrams to represent :
(i) ray AB i.e. \(\overrightarrow { AB } \)
(ii) line AB i.e. \(\overleftrightarrow { AB }\)
(iii) ray BA.

Solution:

Question 14.
Use a ruler and And whether the following points are collinear or not:
(i) D, A and C
(ii) A, B and C
(iii) A, B and E
(iv) B, C and E

Solution:

Question 15.
From the adjoining figure, write:
(i) all pairs f parallel lines
(ii) all the lines which intersect EF.
(iii) lines whose point of intersection is G.

Solution:

Fundamental Concepts Exercise 23B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, which of the following is a plane closed figure :

Solution:

Question 2.
Fill in the blanks :
(i) ….. is a three sided plane closed figure.
(ii) A square is a plane closed figure which is not bounded by …..
(iii) A rectangle is a …. sided plane ……
(iv) A rectangle has opposite sides ….. and adjacent sides ….. to each other.
(v) The sides of a square are ……. to each other and each angle is
(vi) For a line segment, a line making angle of ……… with it, is called perpendicular to it.
(vii) For a line segment, a line ……. it and making angle of ……. with it, is called ……. bisector of the line segment.
(viii) How many perpendiculars can be drawn to a line segment of length 6 cm ?
(ix) How many perpendicular bisectors can be drawn to a line segment of length 6 cm ?
(x) A perpendicular to a line segment will be its perpendicular bisector if it passes through the ……. of the given line segment.
Solution:

Question 3.
State, which of the lines/line- segments are perpendicular to the line PQ :

Solution:

Question 4.
Which of the following figures show two mutually perpendicular lines :

Solution:

Question 5.
For each figure given below name the line segment that is perpendicular bisector of the other :

Solution:

Question 6.
Name three objects from your surroundings that contain perpendicular edges.
Solution:

Question 7.
Using the given figure, answer the following :
(i) Name the pairs of parallel lines.
(ii) Name the pairs of mutually perpendicular lines.
(iii) Is the line p parallel to the line l ?
(iv) Is the line q perpendicular to the line m ?

Solution:

Question 8.
Place a scale (ruler) on a sheet of paper and hold it firmly with one hand. Now draw two line segments AB and CD along the longer edges of the scale. State whether segment AB is parallel to or perpendicular to segment CD.
Solution:

Question 9.
Check your text book :
(i) How many pairs of its edges are parallel to each other ?
(ii) How many pairs of its edges are perpendicular to each other ?
Solution:

Question 10.
Give two examples from your surroundings for each of the following :
(i) intersecting lines
(ii) parallel lines
(iii) perpendicular lines.
Solution:

Question 11.
State true or false; if false, give the correct statement :
(i) The maximum number of lines through three collinear points is three.
(ii) The maximum number of lines through three non-collinear points is three.
(iii) Two parallel lines always lie in the same plane.
(iv) Concurrent lines always meet at the same point.
(v) A surface can be plane or curved.
(vi) There are an infinite number of points in a line segment of length 10 cm.
(vii) There are an infinite number of points in a line.
(viii) A plane has an infinite number of lines.
(ix) A plane has an infinite number of points.
Solution:

Fundamental Concepts Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Mark a point O on a piece of paper. Using a sharp pencil and a ruler, draw a line through the point O. Then draw one more line through the point O. How many lines can you draw through O?
Write a statement regarding your observations.
Solution:

Question 2.
Mark two points A and B on a plain sheet “ of paper. Using a sharp pencil and a ruler, draw a line through points A and B. Try to draw one more line through A and B. What do you observe ?
Write a statement regarding your observations.
Solution:

Question 3.
Draw two straight lines on a sheet of paper so that the lines drawn :
(i) intersect each other.
(ii) do not intersect.
(iii) appear to intersect when extended.
Solution:

Question 4.
Draw a figure to show that :
(i) points A, B and C arc collinear.
(ii) lines AB, CD and EF are concurrent.
Solution:

Question 5.
In your note-book, draw two rays with the same initial point O and going in opposite directions. Write the special name for the final figure obtained.
Solution:

Question 6.
In each figure, given below, write the number of line segments used :

Solution:

Question 7.
In a circle, point P is its centre and PA = PB = radius of the circle. Where do points A and B lie ?
Solution:

Question 8.
Draw a four-sided closed figure, in which:
(i) all the sides are equal and each angle is 90°.
(ii) opposite sides are equal and each angle is 90°.
Write the special name of each figure drawn.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)

Natural Numbers and Whole Numbers Exercise 5A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) Smallest natural number is …………..
(ii) Smallest whole number is …………
(iii) Largest natural number is …………
(iv) Largest whole number is ………..
(v) All natural numbers are …………
(vi) All whole numbers are not …………
(vii) Successor of 4099 is …………..
(viii) Predecessor of 4330 is …………….
Solution:

Question 2.
Represent the following whole numbers on a number line :
0, 3, 5, 8, 10
Solution:

Question 3.
State, true or false :
(i) Whole number are closed for addition.
(ii) If a and b are any two whole numbers, then a + b is not a whole number.
(iii) If a and b are any two whole numbers, then a + b = b + a
(iv) 0 + 18= 18 + 0
(v) Addition of whole numbers is associative.
(vi) 10 + 12 + 16 = (10 + 12) + 16 = 10 + (12 + 16)
Solution:

Question 4.
Fill in the blanks :
(i) 54 + 234 = 234 + …………
(ii) 332 + 497 = ………… + 332
(iii) 286 + 0 = ………..
(iv) 286 x 1 = ……….
(v) a + (b + c) = (a + ………) + c
Solution:

Question 5.
By re-arranging the given numbers, evaluate :
(i) 237 + 308 + 163
(ii) 162 + 253 +338 + 47
(iii) 21 + 22 + 23 + 24 + 25 + 75 + 76 + 77 + 78 + 79
(iv) 1 + 2 + 3 + 4 + 596 + 597 + 598 + 599
Solution:

Question 6.
Is a + b + c = a + (b + c) = (b + a) + c ?
Solution:

Question 7.
Which property of addition is satisfied by :
(i) 8 + 7 = 15
(ii) 3+ (5 + 4) = (3 + 5)+ 4
(iii) 8 x (8 + 0) = 8 x 8 + 8 x 0
(iv) (7 + 6) x 10 = 7 x 10 + 6 x 10
(v) (15 – 12) x 18 = 15 x 18 – 12 x 18
(vi) 16 + 0= 16
(vii) 23 + (-23) = 0
Solution:

Question 8.
State, True or False :
(i) The sum of two odd numbers is an odd number.
(ii) The sum of two odd numbers is an even number.
(iii) The sum of two even numbers is an even number.
(iv) The sum of two even numbers is an odd number.
(v) The sum of an even number and an odd number is odd number.
(vi) Every whole number is a natural number.
(vii) Every natural number is a whole number.
(viii) Every whole number + 0 = The whole number itself.
(ix) Every whole number x 1 = The whole number itself.
(x) Commutativity and associativity are properties of natural numbers and whole numbers both.
(xi) Commutativity and associativity are properties of addition for natural numbers and whole numbers both.
(xii) If x is a whole number then -x is also a whole number.
Solution:

Natural Numbers and Whole Numbers Exercise 5B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Consider two whole numbers a and b such that a is greater than b.
(i) Is a – b a whole number? Is this result always true?
(ii) b – a a whole number? Is this result always true?
Solution:

Question 2.
Fill in the blanks :
(i) 8 – 0 = ……….. and 0 – 8 = ……….
8 – 0 ≠ 0 – 8, this shows subtraction of whole numbers is not ………..
(ii) 5 – 10 = ………., which is not a …………
⇒ Subtraction of ……….. is not closed.
(iii) 7 – 18 = ……….. and (7 – 18) – 5 = …………..
18 – 5 = …………. and (7 – 18) – 5 = ………….
Is (7 – 18) – 5 = 7 – (18 – 5) ?
⇒ Subtraction of whose numbers is not ………….
Solution:

Question 3.
Write the identify number, if possible for subtraction.
Solution:

Question 4.
Write the inverse, if possible for subtraction of whole numbers ?
Solution:

Question 5.
12 × (9 – 6) = ………….. = ………….
12 × 9 – 12 × 6 = …………. = …………….
Is 12 × (9 – 6) = 12 × 9 – 12 × 6 ? ………….
Is this type of result always true ? ……………
Name the property used here …………..
Solution:

Question 6.
(16 – 8) × 24 = ………….. = …………..
16 × 24 – 8 × 24 = …….. – ……….. = ………..
Is (16 – 8) × 24 = 16 × 24 – 8 × 24 ? …………..
Is the type of result always true? ………….
Name the property used here ………………
Solution:

Natural Numbers and Whole Numbers Exercise 5C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 42 × o = ……….
(ii) 592 × 1 = ………..
(iii) 328 × 573 = ……….. × 328
(iv) 229 × ………… = 578 × 229
(v) 32 × 15 = 32 × 6 + 32 × 7 + 32 × ……….
(vi) 23 × 56 = 20 × 56 + ……… × 56
(vii) 83 × 54 + 83 × 16 = 83 × ( ……….. ) = 83 × ………….. = …………
(viii) 98 × 273 – 75 × 273 = ( …………. ) × 273 = ………… × 273
Solution:

Question 2.
By re-arranging the given numbers, evaluate :
(i) 2 × 487 × 50
(ii) 25 × 444 × 4
(iii) 225 × 20 × 50 × 4
Solution:

Question 3.
Use distributive law to evaluate :
(i) 984 × 102
(ii) 385 × 1004
(iii) 446 × 10002
Solution:

Question 4.
Evaluate using properties :
(i) 548 × 98
(ii) 924 × 988
(iii) 3023 × 723
Solution:

Question 5.
Evaluate using properties :
(i) 679 × 8 + 679 × 2
(ii) 284 × 12 – 284 × 2
(iii) 55873 × 94 + 55873 × 6
(iv) 7984 × 15 – 7984 × 5
(v) 8324 × 1945 – 8324 × 945
(vi) 3333 × 987 + 13 × 3333
Solution:

Question 6.
Find the product of the :
(i) greatest number of three digits and smallest number of five digits.
(ii) greatest number of four digits and the greatest number of three digits.
Solution:

Question 7.
Fill in the blanks :
(i) (437 + 3) × (400 – 3) = 397 × ……….
(ii) 66 + 44 + 22 = 11 × (………..) = 11 × ……….
Solution:

Question 8.
Evaluate :
(i) 355 × 18
(ii) 6214 × 12
(iii) 15 × 49372
(iv) 9999 × 8
Solution:

Natural Numbers and Whole Numbers Exercise 5D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Show that :
(i) division of whole numbers is not closed
(ii) any whole number divided by 1, always gives the number itself.
(iii) every non-zero whole number divided by itself gives 1 (one).
(iv) zero divided by any non-zero number is zero only.
(v) a whole number divided by 0 is not defined.
For each part, given above, give an example.
Solution:

Question 2.
If x is a whole number such that x ÷ x = x, state the value of x.
Solution:

Question 3.
Fill in the blanks :
(i) 987 + 1 = …………
(ii) 0 + 987 = ……….
(iii) 336 – (888 + 888) = ……….
(iv) (23 + 23) – (437 + 437) = ………
Solution:

Question 4.
Which of the following statements are true ?
(i) 12 ÷ (6 × 2) = (12 ÷ 6) × (12 ÷ 2)
(ii) a ÷ (b – c) = \(\frac { a }{ b } -\frac { a }{ c }\)
(iii) (a – b) ÷ c = \(\frac { a }{ c } -\frac { b }{ c }\)
(vi) (15 – 13) ÷ 8 = (15 ÷ 8) – (13 ÷ 8)
(v) 8 ÷ (15 – 13) = \(\frac { 8 }{ 15 } -\frac { 8 }{ 13 }\)
Solution:

Natural Numbers and Whole Numbers Exercise 5E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the difference between the largest number of four digits and the smallest number of six digits.
Solution:

Question 2.
Find the difference between the smallest number of eight digits and the largest number of five digits.
Solution:

Question 3.
The product of two numbers is 528. If the product of their unit’s digits is 8 and the product of their ten’s digits is 4 ; find the numbers.
Solution:

Question 4.
Does there exist a number a such that a ÷ a = a?
Solution:

Question 5.
Divide 5936 by 43 to find the quotient and remainder. Also, check your division by using the formula,
dividend = divisor × quotient + remainder.
Solution:

Natural Numbers and Whole Numbers Exercise 5F – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
(i) 1 × 9 + 1 = 10
12 × 9 + 2 = 110
123 × 9 + 3 = 1110
(ii) 9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
(iii) 1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
(iv) 111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
Solution:

Question 2.
Complete each of the following magic squares :

Solution:

Question 3.
See the following pattern carefully :

(i) If n denotes the number of figure and S denotes the number of matches ; find S in terms of n.
(ii) Find how many matches are required to make the :
(1) 15th figure
(2) 40th figure
(iii) Write a discretion of the pattern in words.
Solution:

Question 4.
(i) In the following pattern, draw the next two figures.

(ii) Construct a table to describe the figures in the above pattern.
(iii) If n denotes the number of figure and L denotes the number of matches, find L in terms of n.
(iv) Find how may matches are required to make the :
(1) 12th figure
(2) 20th figure
Solution:

Question 5.
In each of the following patterns, construct next figure.
(i) In each case, if n denotes the number of figure and F denotes the number of matchsticks used, find F in terms of n.
(ii) Also find, in each case, how many matches are required to make the : 16th figure and 30th figure.


Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 4 Place Value

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 4 Place Value

Place Value Exercise 4A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) In 20 kg, the unit is ………….., which is taken …………. times.
(ii) In 80 m, the unit is …………., which is taken …………. times.
(iii) If a unit cm (centimetre) is taken 5 times, the corresponding quantity is …………….
(iv) If a unit km (kilometre) is taken 24 times, the corresponding quantity is ……………
(v)

Number	Numeral	Numeration
53	………….	……….
………	9	…………
240	…………..	………..

Solution:

Question 2.
Fill in the blanks :
(i) In 24,673 ; the place value of 6 is ………..
(ii) In 8,039 ; the place value of 8 is …………..
(iii) In 3,25,648; the local value of 5 is ……………
(iv) In 6,439 ; the local value of 6 is ……….
Solution:

Question 3.
Find the difference between the place values of 3 and 5 in the number 3945.
Solution:

Question 4.
In the number 40562
(i) the local value of 5 = …………..
(ii) the place value of 6 = ………..
(iii) the sum of the place value of 5 and the place value of 6 = …………
Solution:

Question 5.
Read and write the following numbers in words and also in expanded form :
(i) 35,000 = …………
(ii) 76,000 = ……………
(iii) 6,23,000 = ………….
(iv) 40,075 = …………….
(v) 50,004 = ………..
Solution:

Question 6.
Find the difference in the place values of two sevens in the number 8, 72, 574.
Solution:

Place Value Exercise 4B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 999 + 1 = …………
(ii) 10,000 – 1 = …………
(iii) 10 coins – one coin = …………
(iv) ₹ 99 + ₹ 1 = ………..
(v) 10,000 boys – 1 boy = ………..
(vi) 1000 toys – 1 toy = ……….
Solution:

Question 2.
Would the number of students in your school be a 3-digit number or a 4-digit number or a 5-digit number ?
Solution:

Question 3.
Write the smallest number which is just more than 9, 99, 999.
Solution:

Question 4.
Starting from the greatest 5-digit number, write the previous five numbers in descending order.
Solution:

Question 5.
Starting from the smallest 7-digit number, write the next four numbers in ascending order.
Solution:

Question 6.
How many numbers lie between the largest 3-digit number and the smallest 4-digit number ?
Solution:

Question 7.
How many 5-digit numbers are there in all?
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System (With Comparison)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System (With Comparison)

Numbers in India and International System Exercise 3 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the following numerals using Indian System words or International system (as required in words) :
(i) 4, 35, 342 = …………..
(ii) 36, 71, 430 = …………..
(iii) 4, 28, 30, 004 = …………..
(iv) 75, 132, 684 = ……………
(v) 815, 906 = …………….
(vi) 5, 420, 700 = ……………..
Solution:

Question 2.
Write the following numbers, placing the commas, according to Indian system :
(i) 835629 = …………
(ii) 35640254 = …………
(iii) 2826040 = ………
Solution:

Question 3.
Write the following numbers, by placing the commas, according to International system :
(i) 6509820 = ………..
(ii) 428140584 = …………
(iii) 63560981 = ……….
Solution:

Question 4.
Fill in the blanks :
(i) Four lakh sixty seven thousand three hundred six.
= ……………… (In numeral form)
= …………… (In International System)
= ……………. (In International numeration)
(ii) Thirteen lakh forty five.
= ……………. (In numeral form)
= ……………. (In International System)
= ……………. (In International numerals)
Solution:

Question 5.
Fill in the blanks :
(i) Six hundred four thousand eight hundred forty seven.
= ……………. (In numeral form)
= ……………. (In Indian System)
= ……………… (Number name in Indian System)
(ii) Two million three hundred ten thousand one hundred four
= …………….. (In numeral form)
= …………… (In Indian System)
= ……………. (In Indian numeration)
= …………….. (In international numerals)
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 2 Estimation

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 2 Estimation

Estimation Exercise 2A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Round off each of the following to the nearest ten :
(i) 62
(ii) 265
(iii) 543
(iv) 8261
(v) 6294
(vi) 3008
(vii) 72326
Solution:

Question 2.
Round off each of the following to the nearest hundred :
(i) 748
(ii) 784
(iii) 2667
(iv) 5432
(v) 6388
(vi) 59237
Solution:

Question 3.
Round off each of the following to the nearest thousand :
(i) 6475
(ii) 6732
(iii) 5352
(iv) 32568
(v) 9248
(vi) 83294
Solution:

Question 4.
Round off
(i) 578 to the nearest ten.
(ii) 578 to the nearest hundred.
(iii) 4327 to the nearest thousand.
(iv) 32974 to the nearest ten-thousand.
(v) 27487 to the nearest ten-thousand.
Solution:

Question 5.
Round off each of the following to the nearest tens, hundreds and thousands.
(i) 864
(ii) 1249
(iii) 54, 547
(iv) 68, 076
(v) 56, 293
(vi) 7, 293
(vii) 89, 24, 379
Solution:

Question 6.
Round off the following to the nearest tens ;
(i) ₹ 562
(ii) 837 m
(iii) 545 cm
(iv) ₹ 27
Solution:

Question 7.
List all the numbers which can be round off to 30.
Solution:

Question 8.
List all the numbers which can be rounded off to 50.
Solution:

Question 9.
Write the smallest and the largest numbers which are rounded off to 80.
Solution:

Question 10.
Write the smallest and the largest numbers which are rounded off to 130.
Solution:

Estimation Exercise 2B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Estimate the sum of each pair of numbers to the nearest ten :
(i) 67 and 44
(ii) 34 and 87
(iii) 23 and 66
(iv) 78 and 18
(v) 96 and 55
(vi) 76 and 62
(vii) 457 and 175
(viii) 474 and 173
(ix) 527 and 267
Solution:

Question 2.
Estimate the sum of each pair of numbers to the nearest hundred :
(i) 336 and 782
(ii) 546 and 342
(iii) 270 and 495
(iv) 4280 and 5295
(v) 4230 and 2410
(vi) 30047 and 39287
Solution:

Question 3.
Estimate the sum of the following pair of numbers to the nearest thousand:
(i) 53826 and 36455
(ii) 56802 and 22475
Solution:

Question 4.
Estimate the following differences correct to nearest ten :
(i) 82 – 27
(ii) 96 – 36
(iii) 508 – 248
Solution:

Question 5.
Estimate each difference to the nearest hundred :
(i) 769 – 314
(ii) 856 – 687
(iii) 6352 – 2086
Solution:

Question 6.
Estimate each difference to the nearest thousand :
(i) 45974 – 38766
(ii) 76003 – 48399
Solution:

Question 7.
Estimate each of the following products by rounding of each number to the nearest ten :
(i) 49 x 52
(ii) 63 x 38
(iii) 27 x 54
(iv) 53 x 85
(v) 74 x 67
(vi) 25 x 33
Solution:

Question 8.
Estimate each of the following products by rounding off each number to the nearest hundred :
(i) 477 x 213
(ii) 624 x 236
(iii) 333 x 247
(iv) 537 x 283
(v) 382 x 127
(vi) 427 x 328
Solution:

Question 9.
Estimate each of the following products by rounding off the first number correct to nearest ten and the other number correct to nearest hundred :
(i) 28 x 287
(ii) 432 x 128
(iii) 48 x 165
(iv) 72 x 258
(v) 83 x 664
(vi) 44 x 250
Solution:

Question 10.
Estimate each of the following quotients by converting each number to the nearest ten :
(i) 87 ÷ 28
(ii) 84 ÷ 23
(iii) 77 ÷ 22
(iv) 198 ÷ 24
(v) 355 ÷ 26
(vi) 444 ÷ 42
(vii) 843 ÷ 33
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions